Answer:
745
Explanation:
You want the original number of books in the library if adding 298 children's books increased the fraction of children's books from 2/5 to 4/7.
Ratio
We often like to work problems like this in terms of "ratio units." Here, we'll let x represent the number of books in a ratio unit. This means the number of children's books is originally 2x, and the total number of books is originally 5x. Then we have ...
(2x +298)/(5x +298) = 4//7
Solution
Cross multiplying gives ...
7(2x +298) = 4(5x +298)
3(298) = 6x . . . . . . . . . . . . . subtract (14x+4(298))
149 = x
745 = 5x . . . . . . the original number of books in the library
There were 745 books in the library at first.
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Additional comment
If we let x represent the original number of library books, then the arithmetic involves more fractions. You would have an equation like ...
2/5x +298 = 4/7(x +298)
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